What's new

# Miller chapter 3

#### amit.m.sharma

##### Member
I would think it is
mean = 0.7*0 + 0.3*1 = 0.3
variance = 0.7*(0-0.3)^2 + 0.3*(1-0.3)^2 = 0.063 + 0.147 = 0.21
std deviation = sqrt (0.21) = 0.458

#### praveenraj

##### New Member
Also need help with this question as well what is empirical probability if we roll a dice once what is the probability of receiving 3 on a dice (ans 18%)? in normal probability it is 1/6 right?

#### praveenraj

##### New Member
Hi ,

Kindly confirm why empirical probability for resultant 3 on a dice = 18 percent however the normal probability is 1/6 what is the formula for empirical probability?

#### Detective

##### Active Member
Do you mean die or dice? Empirical by definition is experimental, i.e. what is observed in the real world. The probability of rolling a 3 on a six sided die would be 1/6 assuming it’s a fair die, but you can experimentally roll it 100 times and see 3, 18 times, giving you an empirical probability of 18%. If it is indeed a fair die, as the sample increases we get closer to the true, 1/6 probability.

Without further context I cannot comment on the 18% probability further. Is this from a textbook or some article? Where did you get that number?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @praveenraj That's just an example; ie, a single simulation. If we roll a fair die 100 times, we expect 1/6*100 = 16.17, that is we expect about 16 or 17 of each. As a random variable, the fair die has an parametric (aka, analytical, theoretical) distribution that characterizes the population: it is uniform discrete where Pr(X = x) = 1/6. But every simulation of 100 throws produces a sample with non-uniform outcomes. My exhibit above shows one outcome; if we throw another 100, we will get a (slightly) different outcome, but probably not too dramatically different. Most of our realistic work is observing samples and fitting analytical distributions to them; e.g., we observe daily returns and, if they are approximately normal, we fit a (parametric) normal distribution to the observed sample. Thanks,